In geometry, the gyroelongated square cupola is one of the Johnson solids (J<sub>23</sub>). As the name suggests, it can be constructed by gyroelongating a square cupola (J<sub>4</sub>) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J<sub>45</sub>) with one square bicupola removed.
The surface area is
The volume is the sum of the volume of a square cupola and the volume of an octagonal prism,
The dual of the gyroelongated square cupola has 20 faces: 8 kites, 4 rhombi, and 8 pentagons.